Medieval Theories of Obligationes

Obligationes (literally, “obligations”) or disputations
de obligationibus were a medieval disputation format that
became very widespread in the thirteenth and fourteenth centuries.
Although their name might suggest they had something especially to do
with ethics or moral duty, they did not. The purpose of these
disputations was strictly logical. Several kinds of disputations
de obligationibus were distinguished in the medieval
literature. The most widely studied kind to date was called
“positio” (= positing). It is difficult or even impossible to
map the genre to the genres modern logic, but issues involved include
at least counterfactual and per impossibile reasoning, and
dynamic commitment to remain logically consistent. Disputations de
obligationibus appear to lay at the background of the modern
practice of the academic “thesis defense.”

The medieval disputation de obligationibus was a highly
stylized academic disputation form between two parties, an “opponent”
(opponens) and a “respondent” (respondens). From at
least the early thirteenth century, a literature began to appear, in
independent treatises as well as discussions as part of larger works,
on how to conduct such
disputations.[1]
This literature was regarded as belonging to logic, and the study of
obligationes became part of the logic curriculum followed by
undergraduates.[2]
Treatises on obligationes are however not early
works in deontic logic.[3]
The name “obligationes” means in Latin as much as in English
obligation in the sense of “duty,” but what is “obligatory” is
strictly limited to the general logical obligation not to contradict
oneself in a disputation and to a specific logical obligation that the
opponent gives to the respondent in the beginning of the
disputation. Even the general moral duty to be honest and accept what
one believes to be true is limited to a very marginal role in these
highly technical disputations.

Some late-medieval authors claimed that the theoretical basis for
obligationes came from two passages in Aristotle (Prior
Analytics I.13.32a18–20, Metaphysics
IX.4.1047b10–12), both of which say merely that when something
possible is posited, nothing impossible
results.[4]
But these Aristotelian texts may be the historical origin of the
obligationes literature only in a very indirect manner. The
first treatises on obligationes are earlier than the ready
availability of the Metaphysics in Latin translation, and do
not mention either passage. Moreover, while it is certainly true that
obligational disputations never require an impossibility to follow
when a possibility is posited, that fact does not by itself account
for some of the most characteristic features of
obligationes. Indeed, some of the earliest discussions
concern what happens not when a possibility is posited, but when an
impossibility is
posited. [5]

It is precisely this feature, in fact, that at least two early
treatises attribute to
Aristotle[6]:

And Aristotle says this. For he says, “The impossible is to be
posited so that it may be seen what follows on that basis.”

That impossible positing has to be maintained is proved as follows:
For just as we say that the possible is to be conceded so that it may
be seen what follows on that basis, likewise we have it from Aristotle
that the impossible is to be conceded so that it may be seen what
happens on that basis.

It seems thus more probable to connect obligational disputations to
Aristotle's per impossibile arguments, which had been
discussed by at least Boethius and Ibn
Rushd.[8]

In any event, the prehistory of the obligationes literature
cannot be fully explained in terms of these possible sources. For
there were several other kinds or “species” of
obligationes besides “positing.” The early Obligationes
Parisienses, for example, distinguishes six kinds; the same six
are found also in Walter Burley and William of Ockham: positing
(positio), counterpositing (depositio), “let it be
doubted” (dubitetur), institution (institutio), the
truth of the matter (rei veritas), and petition
(petitio).[9]
Apart from “positing,” most of these kinds of obligationes
have been little studied in the modern literature.

The most widely discussed kind of obligatio, both in the
medieval literature and in recent scholarship, is no doubt
positio or “positing.” In a positio the
“opponent” begins by saying “I posit that
p.” The proposition p is called the
“positum.” The “respondent” then says
either “I admit it” or “I deny it,” depending
on certain conditions. For example, the treatises by Roger Swyneshed,
Robert Fland, and Richard Lavenham all stipulate that in order for the
positum to be “admissible,” it must be a
contingent
proposition.[10]
Other authors, as we have seen above, allow the positum to
be an impossible proposition, provided that its impossibility is not
“manifest,” so that the proposition can be entertained and
believed.[11]
We shall not consider such cases here.

If the respondent denies the positum, the disputation is
over before it really gets started. If he admits the positum,
the disputation is under way: The opponent then “proposes” to the
respondent a series of propositions, one after another. To each such
propositum the respondent must reply by saying “I concede it,”
“I deny it,” or “I doubt it,” according to certain
rules.[12]
The rules stipulate that the correct response depends in part on
whether the propositum is “relevant” or “irrelevant”
(pertinens/impertinens), and if it is relevant whether it is
“sequentially relevant” or “incompatibly relevant” (pertinens
sequens/pertinens repugnans). The specification of these notions
and of how they affect the correct response to the propositum
constitutes the kernel of the theory of positio, and varied
from author to author.

Walter Burley's account represents what was perhaps the “default” or
“standard”
theory.[13]
According to
him[14]:

For each step n of the disputation, beginning with the
first propositum as step 1, the propositum is
“sequentially relevant” at step n if and only if it logically
follows from the conjunction of the positum together with any
proposita that have been conceded at earlier steps of the
disputation, and together with the contradictories of any proposita
that have been denied at earlier steps. The propositum is
“incompatibly relevant” at step n if and only if its
contradictory follows from that same conjunction. It is
“irrelevant” at step n if and only if it is neither
sequentially relevant nor incompatibly relevant there.

For each step n of the disputation, and for each
propositum p, the respondent must concede p at step
n if it is sequentially relevant at n, and must deny
it if it is incompatibly relevant at n. If p is
irrelevant at step n, the respondent must reply according to
his knowledge of the actual facts (independent of what is posited in
the disputation). Thus, if p is irrelevant at n and
the respondent knows it is true in fact, he must concede it; if
p is irrelevant at n and the respondent knows it is
false in fact, he must deny it; if p is irrelevant and the
respondent does not know whether it is true or false, he must doubt
it.

The disputation continues until the opponent says “Cedat
tempus,” which can either mean “Time is up!” (the disputation is
over) or “Time out!” In the latter case the disputation is interrupted
temporarily while the opponent points out some mistake in the
respondent's replies or makes some other observation. In both senses,
the point is the same: the respondent is not “obligated” by the rules
of positio except when the “game clock” is
running.[15]

An example will help clarify the rules.

Opponent

Respondent

I posit that Atlanta is the capital of
Pennsylvania.

I admit it.

Comments: Atlanta is not in fact the capital of
Pennsylvania. But that does not prevent the opponent from positing that
it is.

Step 1:

Atlanta is south of the Mason-Dixon Line.

I concede it.

Comments: From the positum it follows neither that
Atlanta is south of the Mason-Dixon Line nor that it isn't. (The
positum says nothing at all about the location of the
Mason-Dixon Line or of Atlanta.) Hence step 1 is irrelevant. Nevertheless, since the
respondent knows that step 1 is in fact true, he must concede it.

Step 2:

The capital of Pennsylvania is south of the
Mason-Dixon Line.

I concede it.

Comments: From the positum and the already conceded
step 1, step 2 follows. Hence it is sequentially relevant and must be
conceded.

Time is up!

Several peculiar things should be noted about these rules. First,
the burden of the rules falls almost entirely on the respondent. As
long as he picks an “admissible” positum to begin with, the
opponent is otherwise free to propose anything he pleases at any step
of the disputation.

Second, note the role of the respondent's epistemic state. It is a
factor in determining the correct replies, but only when the
propositum is irrelevant.

Third, note that order counts. That is, depending on the
order in which proposita are proposed, different replies to them may
be required. Thus if steps 1 and 2 were reversed in the above example,
both would have to be denied:

Opponent

Respondent

I posit that Atlanta is the capital of
Pennsylvania.

I admit it.

Comments: As before.

Step 1:

The capital of Pennsylvania is south of the Mason-Dixon Line.

I deny it.

Comments: From the positum it follows neither that
the capital of Pennsylvania is south of the Mason-Dixon Line nor that
it isn't. (As before, the positum says nothing about the
location of the Mason-Dixon Line or of the capital of Pennsylvania.)
Hence step 1 is irrelevant. Nevertheless, since the respondent knows
that step 1 is in fact false, he must deny it.

Step 2:

Atlanta is south of the Mason-Dixon Line.

I deny it.

Comments: From the positum
and the contradictory of step 1 (step 1 was denied, recall),
the contradictory of step 2 follows. Hence step 2 is incompatibly
relevant and must be denied.

Time is up!

This set of rules guarantees that positio is “consistent”
in each of the following three, progressively stronger
senses[16]:

(1)
No given disputation ever requires the respondent to concede an
impossibility at any one
step.[17]

(2)
No given disputation ever requires the respondent to concede
proposita of the form p and not-p at
different steps.

(3)
No given disputation ever requires the respondent to concede at
different steps each member of an inconsistent set of
proposita.

Yet on Burley's theory positio fails to be
“consistent” in another
sense[18]:

(4)
No given disputation ever requires the respondent to give different
replies to the same propositum at different steps.

As an example of this failure, let p and q be
contingent propositions neither of which logically implies the other,
and let the respondent know that q is false whereas he does
not know the truth value of p. Then:

Opponent

Respondent

I posit that p or
q.

I admit it.

Step 1:

p

I doubt it.

Comments: The positum implies neither p nor
not-p. Step 1 is therefore irrelevant. Thus, since the
respondent does not know its truth value, he must doubt it.

Step 2:

q

I deny it.

Comments: The positum implies neither q nor
not-q. Step 2 is therefore irrelevant. (Since step 1 was
neither conceded nor denied, it does not affect whether step 2 is
relevant or irrelevant.) Since the respondent knows that q
is in fact false, it must be denied.

Step 3:

p

I concede it.

Comments: Step 3 follows from the positum and the
contradictory of step 2 (step 2 was denied, recall). Hence it
must be conceded, even though the same propositum was doubted in step
1.

Time is up!

Clearly, positio on Burley's theory is a very peculiar kind
of disputation.

Burley's theory of positio was not the only one. Another
account seems to have originated with a certain Roger Swyneshed, who
wrote an Obligationes probably sometime after 1330 and
certainly before 1335 (Spade [1977]). This alternative theory was
recognized by Robert Fland, a mid-fourteenth century author about whom
very little is known. Fland reports both Burley's theory and
Swyneshed's theory, calling them the “old response” and the “new
response,” respectively. He does not choose between them, but simply
tells the respondent to pick whichever one he likes (Spade [1980],
§20). Richard Lavenham, on the other hand, a later-fourteenth
century author contemporary with John Wyclif, accepts Swyneshed's
version of positio outright. A certain John of Wesel from
mid-fourteenth century Paris also shows knowledge of Swyneshed's views
(John of Wesel [1996]). Nevertheless, Swyneshed's views seem to have
generated some controversy. For instance, Ralph Strode, in the
later-fourteenth century (roughly contemporary with John Wyclif), heatedly
rejected features of Swyneshed's theory, as did Peter of
Candia and the Logica magna attributed to Paul of Venice
(Spade [1982a], pp. 337–39).

Swyneshed's theory of positio is in many respects like
Burley's, but differs in one major respect. For Swyneshed, in assessing
whether a propositum is relevant or irrelevant, the responses
to previous proposita do not matter. That is, for him, a
propositum is “sequentially relevant” if and only if it
logically follows from the positum alone; it is “incompatibly
relevant” if and only if its contradictory opposite follows from the
positum alone; it is “irrelevant” if and only if it is neither
sequentially nor incompatibly relevant.

Swyneshed's “new response” greatly simplifies the task of the
respondent. He no longer has to keep track of what has previously been
conceded or denied in the disputation. The order in which proposita
are proposed no longer matters. All the respondent has to do is to make
sure he responds appropriately whenever the propositum either
follows from or is inconsistent with the positum alone, and
otherwise just respond according to his knowledge of the actual facts.
As long as he does that, he has performed correctly.

Unlike Burley's theory, Swyneshed's guarantees that positio
is consistent in sense 4
above.[19]
On the other hand, while for Swyneshed positio is consistent
in
sense 1
and
sense 2
above, it fails to be consistent in
sense 3.[20]
For example, suppose you know you are sitting somewhere in Oxford,
and then consider the following positio (Spade [1977],
§100):

Opponent

Respondent

I posit that you are in Rome or you are
running.

I admit it.

Comments: The fact that both disjuncts are false
does not prevent the proposition's being “admissible.”

Step 1:

You are in Rome or you are running.

I concede it.

Comments: This is just a repetition of the positum,
except that here it is not being posited but proposed. It is obviously
sequentially relevant, and so must be conceded.

Step 2:

You are not in Rome.

I concede it.

Comments: Neither step 2 nor its contradictory follows from the
positum alone. Hence it is irrelevant. Since (by hypothesis)
it is also known to be true, it has to be conceded.

Step 3:

You are not running.

I concede it.

Comments: Ditto.

Time is up!

The proposita in steps 1–3 form an inconsistent triad,
and yet each of them has to be conceded in accordance with Swyneshed's
rules.

Burley's and Swyneshed's were not the only theories of
positio, although they seem to have been the most widely
discussed. Other theories were suggested too, but they are not yet
thoroughly studied or
understood.[21]

What was the purpose of positio? The question is not an
easy
one.[22]
For, oddly, although medieval authors themselves speak of
positio as a kind of “disputation,” there seems at first to
be nothing really in dispute! Look back at the preceding
examples. They do not settle, or even try to settle, anything whatever
about the capital of Pennsylvania, the location of the Mason-Dixon
Line, whether you are sitting or running in Rome or in Oxford, or
anything else. Unlike the medieval quaestio format, where
there was a real issue being pursued and a real conflict of opposing
views, there seems to be nothing like that going on in a
positio. What then was its purpose?

Some scholars have suggested that these disputations were
meant as “exercises” or perhaps “examinations” of students' skills. But
skills at doing what? We have just seen that it would not be their
purely logical skills that would be exercised or examined.
What other skills were they? Skills at arguing according to the rules
of obligatio? No doubt, but without some further explanation,
why would anyone want to do that?

One suggestion is that positio might be viewed as something
like a theory of counterfactual
reasoning.[23]
On this account, a
positio would explore “what would happen” if the
positum were true but everything else stayed as much as
possible the same as it really is. This suggestion provides some
rationale for the otherwise mysterious treatment of irrelevant
proposita, where one looks away from the posited situation
back to reality to guide one's responses. In similar fashion, where a
counterfactual hypothesis does not require otherwise, counterfactual
reasoning typically tries to stay as close as possible to reality.

Furthermore, theories of positio bear striking formal
similarities to modern theories of counterfactuals. Transitivity,
contraposition and strengthening the antecedent all fail, and several
other characteristics of counterfactuals seem to be mirrored in the
theory of
positio.[24]

This suggestion has met considerable resistance (Stump [1981] and
[1985], Martin [1993]). One objection is that, at least on Burley's
“standard” theory of positio, if a positum is
possible but nevertheless known to be false, the opponent can maneuver
the respondent into having to concede any proposition whatever
consistent with the positum. Let p be such a
positum, and let q be consistent with
p. Then:

Opponent

Respondent

I posit that p.

I admit it.

Step 1:

Not-p or q.

I concede it.

Comments: If p logically implies q, then step
1 is sequentially relevant, and so has to be conceded. If p
does not logically imply q, step 1 is irrelevant, since
q is by hypothesis consistent with p. In that case,
since p is known to be false, not-p is known to be
true, and step 1 has to be conceded as an irrelevant truth.

Step 2:

q

I concede it.

Comments: The propositumq follows from the
positum and the conceded proposition in step 1. Hence it is
sequentially relevant and must be conceded.

Time is up!

This is a very bad result if positio is a form of
counterfactual reasoning. For it means that, starting from any known
falsehood, one could reason counterfactually to anything
whatever consistent with
it.[25]

Another objection might be that counterfactual reasoning, at least as
we are thinking of it today, does not incorporate epistemic factors in
the way the theory of positio does. It is one thing to say
that we do not know what would happen under a given counterfactual
hypothesis; it is quite another thing to say, as the
“counterfactual”-interpretation has it that the theory
of obligationes does say, that what would happen depends in
part on what we do know in fact.

4.2 Positio and consistency maintainance

In more recent research (e.g. Yrjönsuuri [2009]; Catarina
Dutilh Novaes [2011]), scholars have thought that unlike twentieth
century theories of counterfactual reasoning, obligationes are
characteristically dynamic and dialectical. The core of the art is
that the respondent must use logical skills to keep the general
commitment to consistency. A particular bend to the art comes from the
fact that at least in the late medieval context there was no clear
universally accepted definition what it means to keep consistent in a
dynamic situation. There was, from the viewpoint of this
interpretation, agreement that the consistency at issue in
obligationes is connected to inferential validity. In the
early Obligationes Parisienses the art is explicitly
connected to “knowledge of consequences” (scientia de
consequentiis). Even more generally, it is clear that the kinds
of inferences employed in obligationes are in most cases
strictly logical.

Another suggestion is that positio might lie at the
background of the modern academic practice of the “thesis defense.”
‘Positio’, after all, is just Latin for the Greek
‘thesis’. Furthermore, to this day, the characteristic
terminology of “opponent” and “respondent” is preserved in some
European academic thesis-defenses. Moreover, despite our earlier sense
that there is, oddly, nothing really “in dispute” in a
positio, it is relatively easy to find medieval
discussions—not in treatises or other passages devoted
specifically to the theory of obligationes, but in other
texts—where the characteristic vocabulary and procedures
of positio are appealed to in a context where some substantive
view is being
argued.[26]
That view, however, is not to be found in the positum or in
any of the subsequent proposed steps of the positio. It is
rather a view that the respondent takes himself to know (and
so is prepared to “defend”), and that will therefore affect the
responses he gives to irrelevant proposita. The view being
“defended,” therefore, is not a view explicitly stated anywhere in the
disputation, but a kind of background assumption that underlies the
respondent's replies. This suggestion has some promise, but has not
yet been thoroughly explored. One objection
might be that, despite the initial attractiveness of the fact that
Latin ‘positio’ is the same as Greek
‘thesis,’ this view ends up divorcing the
“thesis” being defended by the respondent from the positum in
the disputation.

The jury is still out. It must be admitted that no one has yet
explained positio, much less the
obligationes-literature in general, in a fully satisfactory
way. An adequate account would have to accommodate

the variety of views of positio one finds in the medieval
literature;

the characteristic treatment of irrelevant proposita, which
brings non-logical factors into play;

in particular, the epistemic factors incorporated into most treatments.

It may be that any adequate account would in effect reproduce the
genre with the terminology of modern logic. That is, perhaps
obligationes are best understood as a logical genre of its
own kind.

Apart from positio, the other kinds of obligatio
recognized in the medieval literature have not been studied nearly so
much. One kind that perhaps needs little separate study is
“counterpositing” (depositio). In effect, if “positing”
requires the respondent to uphold the positum as true (by
conceding what follows from it, etc.), “counterpositing” requires the
respondent to uphold the depositum as false (by denying what
implies it, etc.). In other respects, counterpositing seems,
mutatis mutandis, to be a trivial variation on
positing.[27]
This itself raises an interpretive problem: why treat counterpositing
as a separate kind of obligatio at all?

Another kind that that probably needs only cursory recognition is
“doubting.” Doubting (dubitatio), like counterpositing, is a
variation on positing. In this case, the respondent is required to
uphold the dubitatum as doubtful. (Recall the role of doubtful
irrelevant proposita in a positio.) Again, while the
complications can get get confusing in practice, theoretically this
seems a trivial variation on positing. One wonders again why some
authors singled it out as a separate kind of
obligatio.[28]

A few words should be said about other kinds of obligatio.
Even apart from the context of obligationes, “institution”
(or “imposition”) was regarded as the assigning of meaning to
expressions of language. Within the context of obligationes,
the issue seems to have revolved around how institution or imposition
affected the correct responses in an obligational disputation. Suppose
we call a tail a leg (that is, “impose” the word ‘leg’ to
include tails). How many legs does a lion have? Should we say five, on
the grounds that we are calling tails legs? Or should we continue to
say four, on the grounds that our replies are to be given according to
the meanings words actually have, quite apart from whatever
meanings they might (counterfactually) be assumed to have in the
context of a disputation? (See Spade [1982a], pp. 339–40.)

“Petition” (petitio) has been completely ignored in the
recent literature, and little can be said that is informative about it.
Somewhat more has been said about “the truth of the matter” (rei
veritas), but not much (Spade [1994–1997]).

The vocabulary of medieval obligationes-literature
(“positing,” “conceding,” “admitting,” “relevance/irrelevance”)
appears ubiquitously in late medieval scholastic writings. If not
otherwise, for this reason there is need for more study of the
literature and its role in medieval logic.

Gelber, Hester Goodenough. 2004. It Could Have Been Otherwise:
Contingency and Necessity in Dominican Theology at Oxford,
1300–1350, Leiden: E. J. Brill.

Green, Romuald. 1963. “An Introduction to the Logical Treatise
De obligationibus, with Critical Texts of William of Sherwood
[?] and Walter Burley,” 2 vols. Doctoral dissertation. Katholieke
Universiteit Leuven. A revised version of this essential but
unpublished dissertation has been widely circulated in manuscript form
under the title The Logical Treatise ‘De obligationibus': An
Introduction with Critical Texts of William of Sherwood and Walter
Burley.

John of Wesel [1996]. “Three Questions by John of Wesel
on Obligationes and Insolubilia,”
[Latin edition
available online in PDF,
with introduction and notes, by Paul Vincent Spade.]

Kretzmann, Norman, and Stump, Eleonore. 1985. “The Anonymous
De arte obligatoria in Merton College MS. 306,” in E. P. Bos
(ed.), Medieval Semantics and Metaphysics: Studies Dedicated to
L. M. de Rijk, Ph.D., Professor of Ancient and Mediaeval Philosophy at
the University of Leiden on the Occasion of His 60th
Birthday, Nijmegen: Ingenium, pp. 239–80. (“Artistarium,”
Supplementa, vol. 2.)

Martin, Christopher J. 1990. “Bradwardine and the use
of Positio as a Test of Possibility,” in Simo Knuuttila,
Reijo Työrinoja and Sten Ebbesen (eds.), Knowledge and the
Sciences in Medieval Philosophy: Proceedings of the Eighth
International Congress of Medieval Philosophy, vol. 2. Helsinki:
Publications of the Luther-Agricola Society, pp. 574–85.

––– 1993. “Obligations and Liars,”
in S. Read (ed.), 1993, Sophisms in Mediaeval Logic and Grammar:
Acts of the Ninth European Symposium for Medieval Logic and Semantics,
held at St Andrews, June 1990, Dordrecht: Kluwer,
pp. 357–81. (“Nijhoff International Philosophy
Series,” vol. 48.) (Revised version in Martin [1999].)

––– 1982b. “Three Theories
of Obligationes: Burley, Kilvington and Swyneshed on
Counterfactual Reasoning,” History and Philosophy of Logic, 3:
1–32. Reprinted with the same pagination in Spade 1988, item
XVII.